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This paper studies the incompressible limit of global strong solutions to the three-dimensional compressible Navier-Stokes equations associated with Navier's slip boundary condition, provided that the time derivatives, up to first order, of…

Analysis of PDEs · Mathematics 2013-09-03 Yaobin Ou , Dandan Ren

We construct a local in time spatially real-analytic solution to the 2D and 3D stochastic Navier--Stokes equation driven by a spatially real-analytic multiplicative and transport noise but emanating from an initial condition that is only…

Analysis of PDEs · Mathematics 2024-07-15 Dan Crisan , Prince Romeo Mensah

We consider shape and topology optimization for fluids which are governed by the Navier--Stokes equations. Shapes are modelled with the help of a phase field approach and the solid body is relaxed to be a porous medium. The phase field…

Optimization and Control · Mathematics 2015-04-27 Harald Garcke , Claudia Hecht , Michael Hinze , Christian Kahle , Kei Fong Lam

We consider a projection method for time-dependent incompressible Navier-Stokes equations with a total pressure boundary condition. The projection method is one of the numerical calculation methods for incompressible viscous fluids often…

Numerical Analysis · Mathematics 2021-06-03 Kazunori Matsui

Navier-Stokes equations are investigated in a functional setting in 3D open sets, bounded or not, without assuming any regularity of the boundary. The main idea is to find a correct definition of the Stokes operator in a suitable Hilbert…

Analysis of PDEs · Mathematics 2007-05-23 Sylvie Monniaux

This work presents a non-linear extension of the high-order discretisation framework based on the Variational Multiscale (VMS) method previously introduced for steady linear problems. We build on the concept of an optimal projector defined…

Numerical Analysis · Mathematics 2025-12-22 Suyash Shrestha , Marc Gerritsma , Gonzalo Rubio , Steven Hulshoff , Esteban Ferrer

We consider a velocity tracking problem for the Navier-Stokes equations in a 2D-bounded domain. The control acts on the boundary through a injection-suction device and the flow is allowed to slip against the surface wall. We study the…

Analysis of PDEs · Mathematics 2017-06-20 Nikolai V. Chemetov , Fernanda Cipriano

We present an adaptive finite element method for the incompressible Navier--Stokes equations based on a standard splitting scheme (the incremental pressure correction scheme). The presented method combines the efficiency and simplicity of a…

Numerical Analysis · Mathematics 2012-05-15 Kristoffer Selim , Anders Logg , Mats G. Larson

We study a generalization of the Navier-Stokes-Fourier system for an incompressible fluid where the deviatoric part of the Cauchy stress tensor is related to the symmetric part of the velocity gradient via a maximal monotone 2-graph that is…

Analysis of PDEs · Mathematics 2017-05-02 Erika Maringová , Josef Žabenský

The nonconforming Morley-type virtual element method for the incompressible Navier-Stokes equations formulated in terms of the stream-function on simply connected polygonal domains (not necessarily convex) is designed. A rigorous analysis…

Numerical Analysis · Mathematics 2022-12-06 D. Adak , D. Mora , A. Silgado

We present a hybrid spectral element-Fourier spectral method for solving the coupled system of Navier-Stokes and Cahn-Hilliard equations to simulate wall-bounded two-phase flows in a three-dimensional domain which is homogeneous in at least…

Fluid Dynamics · Physics 2018-10-10 S. H. Challa , S. Dong , L. D. Zhu

In this paper we study traveling wave solutions to the free boundary incompressible Navier-Stokes system with generalized Navier-slip conditions. The fluid is assumed to occupy a horizontally infinite strip-like domain that is bounded below…

Analysis of PDEs · Mathematics 2023-11-06 Junichi Koganemaru , Ian Tice

A general methodology is presented to perform direct numerical simulations of particle dispersions in a shear flow with Lees-Edwards periodic boundary conditions. The Navier-Stokes equation is solved in oblique coordinates to resolve the…

Soft Condensed Matter · Physics 2012-11-07 Hideki Kobayashi , Ryoichi Yamamoto

We consider the shape optimization of an object in Navier--Stokes flow by employing a combined phase field and porous medium approach, along with additional perimeter regularization. By considering integral control and state constraints, we…

Optimization and Control · Mathematics 2018-12-04 Harald Garcke , Michael Hinze , Christian Kahle , Kei Fong Lam

High-order time-stepping schemes are crucial for simulating incompressible fluid flows due to their ability to capture complex turbulent behavior and unsteady motion. In this work, we propose a third-order accurate numerical scheme for the…

Numerical Analysis · Mathematics 2025-12-22 Kelong Cheng , Jingwei Sun , Hong Zhang

The incompressible Navier-Stokes equations are solved in a channel, using a Discontinuous Galerkin method over staggered grids. The resulting linear systems are studied both in terms of the structure and in terms of the spectral features of…

Numerical Analysis · Mathematics 2021-12-07 Mariarosa Mazza , Matteo Semplice , Stefano Serra-Capizzano , Elena Travaglia

In this study, a shape optimization problem for the two-dimensional stationary Navier--Stokes equations with an artificial boundary condition is considered. The fluid is assumed to be flowing through a rectangular channel, and the…

Optimization and Control · Mathematics 2021-08-10 John Sebastian H. Simon , Hirofumi Notsu

In this paper, we introduce a method of imposing asymmetric conditions on the velocity vector with respect to independent variables and a method of moving frame for solving the three dimensional Navier-Stokes equations. Seven families of…

Fluid Dynamics · Physics 2007-06-28 Xiaoping Xu

This work is a continuation of the analysis first presented in Cheung & Zaki (2014). In that study, the combination matrix was introduced as a means to tractably handle the nonlinear terms in the spectral domain. In this work, a different…

Fluid Dynamics · Physics 2016-05-17 Lawrence C. Cheung , Tamer A. Zaki

The Kleiser-Schumann algorithm has been widely used for the direct numerical simulation of turbulence in rectangular geometries. At the heart of the algorithm is the solution of linear systems which are tridiagonal except for one row. This…

Fluid Dynamics · Physics 2015-11-10 Divakar Viswanath